Automation and Robotics Part 9 potx

Automation and Robotics 194 3. The fuzzy algorithm The Thermo-Mechanical Model has the next control inputs: the valve effective area air flow, eq. (1). u = [A 1 , A 2 , A 3 ] (1) Where A 1 , A 2 and A 3 , are the valve area of cylinder side, rod side, and air return, respectively. However the value of A 1 and A 2 are the same. 3.1 The fuzzy algorithm proposal Figure 3 shows the control block diagram used for the pneumatic actuator system, taking the θ angle as the mechanical system output. Fig. 2. The fuzzy controller proposal for pneumatic position. Equation (2), shows the error equation; the eqs. (3) and (4) shows the proportional valve open level, obtained with a fuzzy logic method, where θ p is the reference and θ is the actual position of the arm. e = θ p - θ (2) [A 1 , A 3 ] = fuzzy(θ p ,θ,e) (3) A 2 = A 1 (4) Next, the fuzzy rules used to solve the problem are presented. 3.2 The fuzzy rules Before the rule settings, both inputs and outputs variables were specified, and are showed in table 1. Input Output Reference, θ p Valve 1, A 1 Angle, θ Valve 2, A 3 Error, e Table 1. Fuzzy rules, inputs and outputs. The membership functions used in the fuzzy process are showed in figures 3 to 5. The used membership functions for the input variables, called reference and angle are the same; and the membership functions for the output variables called valve open A 1 and A 2 , are the same. Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 195 -80 -60 -40 -20 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 Reference Memberships for ERROR WE I G HT ANGLE UP NEG2 POS 2 DOWN -4 -3 -2 -1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Reference Memberships for ERROR WE I G HT ANGL E NEG1 ZERO POS1 (a) (b) Fig. 3. Membership functions for ERROR input. (a) The external part. (b) The internal interval. -80 -60 -40 -20 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 Reference Memberships for REFERENCE WE I G HT ANGLE LOW HALF UP (a) -80 -60 -40 -20 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 Reference Memberships for ANGLE WE I G HT ANGLE LOW HALF UP (b) Fig. 4. Memberships functions. (a) Reference input. (b) Angle input -0.01 0 0.01 0.02 0.03 0. 04 0.05 0.06 0.07 0. 08 0.09 0 0.2 0.4 0.6 0.8 1 Reference Memberships for A1 WEIGHT ANGLE ZERO FEW HALF ALL -0.01 0 0.01 0.02 0.03 0.04 0.05 0. 06 0.07 0.08 0.09 0 0.2 0.4 0.6 0.8 1 Reference Memberships for A2 WEIGHT ANGLE ZERO FEW HALF ALL (a) (b) Fig. 5. Membership functions for the valve values. (a) Valve 1. (b) Valve 2. Automation and Robotics 196 These membership functions are used to control the pneumatic actuator on the manipulator system. In the fuzzy process, the control needs 26 rules, and those rules are distributed depending of the interval of each variable. Table 5 shows the fuzzy rules used to control the pneumatic actuator position. The values for A 1 and A 3 are normalized, that is, a value of 1.0 represents a 100% open valve (completely open); a 0.5 represents a 50% open valve and 0% means the valve is completely closed. INPUT OUTPUT Reference Angle Error A 1 A 2 LOW LOW NEG2 FEW FEW LOW LOW NEG1 FEW ZERO LOW LOW ZERO ZERO ZERO LOW LOW ZERO ZERO ZERO LOW LOW POS1 FEW ZERO LOW LOW POS2 FEW FEW LOW HALF DOWN HALF FEW LOW UP DOWN ALL HALF HALF LOW UP HALF FEW HALF HALF UP FEW FEW HALF HALF NEG2 FEW FEW HALF HALF NEG1 FEW ZERO HALF HALF ZERO ZERO ZERO HALF HALF POS1 FEW FEW HALF HALF POS2 FEW FEW HALF HALF DOWN HALF FEW HALF UP DOWN HALF HALF UP UP UP FEW FEW UP UP NEG1 FEW ZERO UP UP NEG2 FEW FEW UP UP ZERO ZERO ZERO UP UP POS1 FEW ZERO UP UP POS2 FEW FEW UP HALF UP HALF HALF UP LOW UP HALF HALF Table 2. Set of fuzzy rules used in the control process. 3.3 Experimental description Figure 6 shows a functionally block diagram of the system. The ADC is a 12-bit ADS7841 device, with a synchronous serial interface communication, 4-channel and up to 200 KHz conversion rate. The DAC is a 12-bit DAC7624 device, with quad voltage output, parallel input data and 10 µs of settling time. Both DAC and ADC are manufactured by Texas Instruments. The DAC is used to control the proportional valve, and the ADC is used to read the flexible arm position with a 10KΩ resistive sensor, which output value has an interval of 0 to 2 V. Finally, an FPGA is used to implement the digital interfaces with the personal computer, and the PD FPGA based controller. Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 197 Fig. 6. Control block diagram for single-link flexible manipulator with pneumatic actuator. Figure 7 shows a block diagram of hardware description to be implemented into FPGA, such as DAC driver, ADC driver, 50 ms sample time generator, communication protocol controller (RS232 driver), a register to load the DAC input (Register) and the finite state machine to synchronize each module (FSM control). Fig. 7. Hardware description for FPGA block diagram. The FPGA is used to implement the digital interface to control the flexible manipulator robot prototype that is shown in figure 8. Figure 9 shows the hardware used to control the flexible manipulator development. Fig. 8. Flexible manipulator robot prototype. (a) General view. (b) Impulse mechanism. (c) Position sensor. Automation and Robotics 198 Fig. 9. Hardware used for flexible manipulator control. VEA252 power board must be supplied with 24 V dc and the control signal should have ground isolation. For that, an HCNR200 device, manufactured by Hewlett Packard, is used. 4. Results To test the behavior of the system, a set points vector was used, as shows the eq. (2). θ p = [8, 40, 70, 95] (2) Figure 10 shows the fuzzy control simulation results, in comparison with practical results. The values for open valve are small, due to the air pressure; if the valve open are high, the actuator goes up too fast and arrive to the top in less than one second; in simulation way, the maximum value for the valves was established in 10%. This result was compared with practical results of the Fuzzy control. 0 20 40 60 80 100 120 140 0 8 40 70 95 Fuzzy Control Results X [mm] Time [s] Rod Reference Practical result Simulation Fig. 10. Fuzzy control behavior of the flexible arm. The pneumatic actuator is used to generate a flexible manipulator arm displacement in radial way. To control the air flow through the cylinder, a fuzzy logic algorithm was implemented. In figure 10, the system response at the end of cylinder, must be improved. That behaviour is due to the gravity influence on the arm, the valves response and mechanical structure. The behaviour of figure 10 shows several step responses, and speed profile must be developed to obtain better results. Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 199 5. Conclusions and future work The pneumatic actuator is used for the arm position, and to control the air flow through the cylinder, a fuzzy logic algorithm was tested in simulation and practical process, with satisfactory results. The Fuzzy control works only with the percent of valve open, to limit the air flow from the compressor trough the cylinder chambers. The values for A1 and A2 are the same, but different for A 3 . Actually A 3 must be small than A1 to get a better system response. In this case, we can see that a single Fuzzy Logic control is not enough to get a soft behaviour of the system, and a PID algorithm must be used. The system has been tested using several step functions, but a speed profile developing is necessary to improve the system response. The innovation of this work is the application of artificial intelligence control for one-link flexible arm position, with pneumatic cylinder, instead of electrical or hydraulic actuator. The contribution is the base of the knowledge about flexible manipulators with pneumatic actuator and fuzzy logic application. As future work, is considering the use of reference frame, neuronal networks and maybe a combination of those controllers. By other hand, a speed profile should be developed. 9. References Moore P. y J. Pu; Progression of servo pneumatics toward advanced applications; Fluid Power Circuit, Component and System Design; K. Edge and C. Burrows, Eds. Boldock, U. K.: Research Studies Press; pages 347 to 365; 1993. Ramos, J.M.; Gorrostieta, E.; Vargas, E.; Pedraza, J.C.; Romero, R.J.; Piñeiro, B. Pneumatic cylinder control for a flexible manipulator robot. 12th IEEE International Conference on Methods and Model in Automation and Robotics, Miedzyzdroje, Poland, 28 – 31 August 2006a; ISBN 978-83-60140-88-8. Ramos, J.M.; Vargas, E.; Gorrostieta, E.; Romero, R.J.; Pedraza, J.C. Pneumatic Cylinder Control PID for Manipulator Robot; 2006 International Conference on Dynamics, Instrumentation and Control; Queretaro, México, August 13-16 2006b. Suarez, L.; Luis, S. Estrategias de Control Adaptable para el posicionamiento continuo de Cilindros Neumáticos. XI Convencion Informatica 2005; La Habana, Cuba; ISBN 959-7164-87-6; 2005. Wang, J.; Wang, J. D. Identification of Pneumatic Cylinder Friction Parameters using Genetic Algorithms. IEEE Transactions on Mechatronics; vol. 9, no. 1; pages 100 to 107; 2004. Jozsef, K.; Claude, J. Dynamics Modelling and Simulation of Constrained Robotic System. EEE/ASME Transactions on Mechatronics; vol. 8, no. 2; pages 165 to 177; 2003. Henri, P.; Hollerbach, J.M. An Analytical and Experimental Investigation of a Jet Pipe controlled electro-pneumatic Actuator. IEEE Transactions on Robotics and Automation; vol. 14, no. 4; pages 601 to 611; 1998. Feliu, V.; García, A.; Somolinos, J.A. Gauge-Based Tip Position Control of a New Three – Degree-Freedom Flexible Robot. The International Journal of Robotics Research; vol. 20, no. 8; pp. 660-675; August 2001. Mirro, J.; Automatic Feedback Control of a Vibrating Flexible Beam; MS Thesis, Department of Mechanical Engineering, Massachussets Institute of Technology, August 1972. Automation and Robotics 200 Whitney, D.E.; Book, W.J.; Lynch, P.M. Design and Control Considerations for Industrial and Space Manipulators; Proceedings of the Joint Automatic Control Conference, June, 1974. Burrows, C.R.; Webb C.R. Simulation of an On – Off Pneumatic Servomechanism; Automatic Control Group, 1968. Quiles, E.; Morant, F.; García, E.; Blasco, R.; Correcher, A. Control Adaptivo de un Sistema de Control Neumatico. 3ra. Conferencia Iberoamericana en Sistemas, Cibernetica e Informatica CISCI, Julio 2004. Burbano, J.C.; Bacca, G.; Hoyos, M. Control de Posicion y Presion para Manipulador Neumatico a traves de PC. Scientia Et Tecnica, UTP; vol. 21, pp. 71-76; 2003. Pérez, J. Analisis Dinamico de Mecanismos Accionados Neumaticamente. Ph.D. Thesis; Facultad de Ingeniería Mecanica, Electrica y Electronica, FIMEE; Salamanca, Gto.; March 2003. Kiyama, F.; Vargas, J. Modelo Termo-Mecanico para un Manipulador tipo Dielectrico. Informacion Tecnologica; vol. 15; no 5; pages 23 to 31; 2004; ISSN 0716-8756. Feliu, V.; Garcia, A. Gauge-Based tip Position Control of a New Three Degree of Freedom Flexible Robot. The International Journal of Robotics Research; vol. 20, no. 8; pp. 660-675; 2001. Ramos, J.M.; Vargas, J.E.; Gorrostieta, E.; Pedraza, J.C. Nuevo Modelo Polinomial del Comportamiento de un Cilindro Neumatico. Revista Internacional Informacion Tecnologica; vol. 17, no. 3; ISSN 0716-8756; 2006. 12 Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control Dan Selişteanu, Emil Petre, Dorin Popescu and Eugen Bobaşu Department of Automation and Mechatronics, University of Craiova Romania 1. Introduction Nowadays, the domain of biotechnology is characterized by rapid changes in terms of novelty and by highly complex processes that require advanced procedures for design, operation and control. From the engineering point of view, the control of bioprocesses poses a number of challenging problems. These problems arise from the presence of living organisms, the high complexity of the interactions between the micro-organisms, as well as the high complexity of the metabolic reactions. Moreover, for monitoring and control applications, only a few measurements are available, either because the measuring devices do not exist or are too expensive, or because the available devices do not give reliable measurements. Therefore, we can deduce that the main difficulties arising in the control of bioprocesses arrive from two main sources: the process complexity and the difficulty to have reliable measurements of bioprocess variables (Bastin & Dochain, 1990; Selişteanu et al., 2007a). In order to overcome these difficulties several strategies for the control of bioprocesses were developed, such as adaptive approach (Bastin & Dochain, 1990; Mailleret et al., 2004), vibrational control (Selişteanu & Petre, 2001; Selişteanu et al., 2007a), sliding mode control (Selişteanu et al., 2007a; Selişteanu et al., 2007b), fuzzy and neural strategies etc. Sliding mode control (SMC) has been widely accepted as an efficient method for control of uncertain nonlinear systems (Utkin, 1992; Slotine & Li, 1991; Edwards & Spurgeon, 1998). The classical applications of SMC (such as robotics, electrical machines etc.) were extended to SMC of chemical processes (Sira-Ramirez & Llanes-Santiago, 1994) and to SMC of bioprocesses (Selişteanu et al., 2007a; Selişteanu et al., 2007b). The well-known advantages of the SMC are the robustness, controller order reduction, disturbance rejection, and insensitivity to parameter variations. The main disadvantage of the SMC strategies used in real applications remains the chattering phenomenon, even if some techniques of chattering reduction were developed (Slotine & Li, 1991; Edwards & Spurgeon, 1998). Vibrational control (VC) is a non-classical open-loop control method proposed by Bellman, Bentsman and Meerkov (Meerkov, 1980; Bellman et al., 1986a; Bellman et al., 1986b). Applications of the vibrational control theory can be found for: stabilization of plasma, lasers, chemical reactors, biotechnological processes (Selişteanu et al., 2007a) etc. The VC technique is applied by oscillating an accessible system component at low amplitude and high frequency. Therefore, this technique can be considered, like the SMC, a form of high- frequency control (obviously high-frequency relative to the natural frequency of the system). Automation and Robotics 202 But, unlike the SMC, the amplitude and the frequency of the control input are constants and independent of the state of the system, so this technique is a form of open-loop control. In this chapter, which is an extended work of (Selişteanu et al., 2007a), two nonlinear control strategies for bioprocesses are designed: a feedback SMC law and a vibrational control strategy. First, a class of bioprocesses is briefly analysed and a nonlinear prototype model is presented in detail. Then, the design of a feedback control law for a prototype bioprocess is developed. The design is based on a combination between exactly linearization, sliding mode control, and generalized observability canonical forms. In order to implement this SMC law, asymptotic observers (Bastin & Dochain, 1990) will be used for the reconstruction of unmeasured states. The next paragraph deals with the presentation of most important results of vibrational control theory. Also, a VC strategy for a continuous bioprocess is developed. The existence and the choice of stabilizing vibrations, which ensure the desired behaviour of the bioprocess are analysed. Some simulations results, comparisons of the proposed nonlinear control strategies, and final remarks are also presented. 2. Nonlinear dynamical models of the bioprocesses 2.1 The dynamical model of a class of bioprocesses In bioindustry, the bioprocesses take place in biological reactors, also called bioreactors. A bioreactor is a tank in which several biological reactions occur simultaneously in a liquid medium (Bastin & Dochain, 1990). These reactions can be classified into two classes: microbial growth reactions and enzyme-catalysed reactions. The bioreactors can operate in three modes: the continuous mode, the fed-batch mode and the batch mode. For example, a Fed-Batch Bioreactor (FBB) initially contains a small amount of substrates and micro- organisms and is progressively filled with the influent substrates. When the FBB is full the content is harvested. By contrast, in a Continuous Stirred Tank Bioreactor (CSTB) the substrates are fed to the bioreactor continuously and an effluent stream is continuously withdrawn from the reactor such that the culture volume is constant. In practice, the bioprocess control is often limited to regulation of the temperature and pH at some constant values favourable to the microbial growth. There is however no doubt that the control of the biological state variables (biomass, substrates, products) can help to increase the bioprocess performance. In order to develop and apply advanced control strategies for these biological variables, obviously is necessary to obtain a useful dynamical model. The modelling of bioprocesses is a difficult task; however, using the mass balance of the components inside the bioreactor and obeying some modelling rules, a dynamical state-space model can be obtained (Bastin & Dochain, 1990; Bastin, 1991). A process carried out in a bioreactor can be defined as a set of m biochemical reactions involving n components (with mn ≥ ). The reaction scheme of a bioprocess (the reaction network) contains n components and m reactions. The concentrations of the physical components will be denoted with the notations n,1i, i =ξ . The reaction rates will be denoted as m,1j, j =ϕ . The evolution of each component is described by the differential equation (Bastin & Dochain, 1990): ( ) ∑ −+ξ−ϕ±=ξ i~j iiijiji QFDk  (1) [...]... linearizing strategy (Bastin & Dochain, 199 0), adaptive control (Bastin & Dochain, 199 0; Bastin, 199 1; Dochain & Vanrolleghem, 2001) and so on The exact linearizing control does not work when the kinetics are imprecisely known because the exact cancellation of the nonlinearities would not be possible The performance of adaptive control decreases when large and abrupt changes occur in bioprocess parameters... (Utkin, 197 8; Sira-Ramirez & Llanes-Santiago, 199 4)) The basic idea for the design of the SMC law (20) is to use the auxiliary output σ = 0 as a sliding surface, and so to force the system trajectories to remain on this surface Remark 2 In the case of a static SMC law, the inherent chattering can be reduced using various continuous approximations of the SMC (Slotine & Li, 199 1; Edwards & Spurgeon, 199 8;... so-called sampled SMC (Sira-Ramirez & Llanes-Santiago, 199 4) To reach a good compromise between small chattering and tracking precision a range of other compensation strategies have been proposed, such as integral sliding mode control, sliding mode control with time-varying boundary layers (Slotine & Li, 199 1), fuzzy sliding mode control (Palm et al., 199 7) and complementary SMC (Su & Wang, 2002) 3.2 Design... T (16) is full rank (Fliess, 199 0; Sira-Ramirez, 199 2; Sira-Ramirez & Llanes-Santiago, 199 4) It is easy to verify, after some straightforward calculations, that the rank of the observability matrix is equal to 2 (full rank), except on line ξ 1 = 0 , which is devoid of practical significance ( ξ1 represents the biomass concentration; so ξ 1 = 0 means no micro-organisms and the life in the bioreactor... (Fliess, 199 0)) The inverse of this transformation is obtained by solving (17) with respect to ξ 1 and ξ 2 One can obtain also the transformed system equations, which are of the form: z1 = z2 z 2 = ψ (z 1 , z 2 , u ) y = z1 where ψ is a nonlinear function of state variables and of the input For the design of SMC, consider now the auxiliary output function (the sliding surface): (18) 208 Automation and Robotics. .. kinetics In order to achieve the change of coordinates, a partition of the state vector ξ in two parts is considered This partition denoted (ξa , ξ b ) induces partitions of the yield matrix K: (Ka, Kb), also of the rate vectors F and Q: (Fa, Fb), (Qa, Qb) accordingly We suppose that a state partition is chosen such that the submatrix K a is full rank and dim( ξ a ) = rank(K a ) = rank(K ) Then a linear... vibrational control was developed by Bellman, Bentsman and Meerkov (Meerkov, 198 0; Bellman et al., 198 6a; Bellman et al., 198 6b), who presented the criteria for vibrational stabilizability and vibrational controllability of linear and nonlinear systems Consider a nonlinear system given by the equation: x = f (x , α ) (27) with f:ℜ n × ℜ m → ℜ n , x ∈ ℜ n is a state and α ∈ ℜ m is a parameter, in fact a vector... + F − Q (2) This model describes in fact the behaviour of an entire class of biotechnological processes and is referred to as the general dynamical state-space model of this class of bioprocesses (Bastin & Dochain, 199 0; Bastin, 199 1) In (2), the term K ⋅ ϕ(ξ) is in fact the rate of consumption and/ or production of the components in the reactor, i.e the reaction kinetics The term −Dξ + F − Q represents... of the vectors of measured states ζ 1 and unmeasured states ζ 2 : z = G1 ⋅ ζ 1 + G2 ⋅ ζ 2 (23) with G1 and G2 well defined matrices If the matrix G2 is left invertible, the asymptotic observer equations for (2) derive from the structure of equations (22) and (23): ˆ ˆ z = −D ⋅ z + G ⋅ (Fa − Q a ) + Fb − Q b ˆ = G + ⋅ (z − G ζ ) ˆ ζ 2 2 1 1 (24) 210 Automation and Robotics where G + = (G T G 2 ) −1 G... (Isidori, 199 5) and by imposing a SMC action that stabilize the output The control strategy is obtained by repeated output differentiation and by imposing a discontinuous feedback controller, which drives the output of the system to satisfy a stable linearized dynamics; for Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control 207 details see (Sira-Ramirez, 199 2; Sira-Ramirez . Li, 199 1; Edwards & Spurgeon, 199 8). Vibrational control (VC) is a non-classical open-loop control method proposed by Bellman, Bentsman and Meerkov (Meerkov, 198 0; Bellman et al., 198 6a;. linearizing strategy (Bastin & Dochain, 199 0), adaptive control (Bastin & Dochain, 199 0; Bastin, 199 1; Dochain & Vanrolleghem, 2001) and so on. The exact linearizing control does. Spurgeon, 199 8). The classical applications of SMC (such as robotics, electrical machines etc.) were extended to SMC of chemical processes (Sira-Ramirez & Llanes-Santiago, 199 4) and to SMC